Which of the following numbers is a factor of 117? ${4,5,11,13,14}$
Answer: By definition, a factor of a number will divide evenly into that number. We can start by dividing $117$ by each of our answer choices. $117 \div 4 = 29\text{ R }1$ $117 \div 5 = 23\text{ R }2$ $117 \div 11 = 10\text{ R }7$ $117 \div 13 = 9$ $117 \div 14 = 8\text{ R }5$ The only answer choice that divides into $117$ with no remainder is $13$ $ 9$ $13$ $117$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $13$ are contained within the prime factors of $117$ $117 = 3\times3\times13 13 = 13$ Therefore the only factor of $117$ out of our choices is $13$. We can say that $117$ is divisible by $13$.